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We propose an improved methodology to constrain spatial variations of thefine structure constant using clusters of galaxies. We use the {\it Planck}2013 data to measure the thermal Sunyaev-Zeldovich effect at the location of618 X-ray selected clusters. We then use a Monte Carlo Markov Chain algorithmto obtain the temperature of the Cosmic Microwave Background at the location ofeach galaxy cluster. When fitting three different phenomenologicalparameterizations allowing for monopole and dipole amplitudes in the value ofthe fine structure constant we improve the results of earlier analysisinvolving clusters and the CMB power spectrum, and we also found that thebest-fit direction of a hypothetical dipole is compatible with the direction ofother known anomalies. Although the constraining power of our current datasetsdo not allow us to test the indications of a fine-structure constant dipoleobtained though high-resolution optical/UV spectroscopy, our results dohighlight that clusters of galaxies will be a very powerful tool to probefundamental physics at low redshift.

Constraining spatial variations of the fine structure constant using clusters of galaxies and Planck data